I have thought about cutting rolls by laser light too, from time to
time.  I am not familiar with laser properties as regards white paper
reflectance.  I don't know how much energy a white sheet of paper would
reflect, but this would probably vary according to the laser wave-
length.  It sounds like one of those situations where anything will
probably cut the paper, but the cost factor of certain lasers, the
lensing capability, and availability from surplus would determine which
one to use.

(I have heard of an idea to shoot down ICBM's with power lasers.  It
has always been a question with me why someone could not deflect laser
energy with a mirror coating over an ablative ceramic shield, or some
other reflecting scheme?)

In moving the beam, one suggestion was a table mount that would
physically move the laser and its cables.  That seems like it would
work, but it also seems to me that the work required to zip a laser
head back and forth at the speed required to cut a roll in less than a
few days' time, would finally take a toll.  The larger and heavier
something is, when moving quickly and stopping instantly, the less
precision you can make it, and the more work it takes to maintain it.

I have seen a nice light beam chart recorder that had a fixed light
source and the beam, being weightless, could traverse the sheet of paper
without inertia slowing it down, just by using a combination of
rotating mirror and cylindrical lens.  So you could either spin a
multi-sided first-surface mirror or a prism at a high rate of speed,
firing the laser according to the position of the mirror to make a hole
slot which can then be advanced and zapped again and again, or the
mirror could be incremented to send the light in steps across the page
row, and could stay in one position until the hole was fully burned.

A single sensor lensed to a Lucite rod (with protection) at the burn
line would tell the machine to advance as soon as it saw the light from
the raw laser beam.  So row advance would be armed by a clear signal
from the sensor.  To me, that's more sure than a simple timer, which
would ignore paper density changes and multiple sheet compression
variables.  You could automatically adjust the burn time required,
depending on the number of sheets and their weight and color.

In the case of a low-cost surplus laser from, say, Milligan and
Higgins, if possibly the cross-sectional area of the beam happens to
be a little too large, the light may not be intense enough to fully
vaporize the paper, so in that case, a crisscross cylindrical lens
system first or whatever is available from surplus (to focus the beam
to a very tiny speck of a point), and then maybe a vibrating gimbal
created with a speaker coil to keep the mirror system wobbling one axis
end of the incremental or rotating mirror might be used to move the
light up and down the same direction the roll runs, to "hog out" the
hole.  The movement could be guided to be circular, and the tiny point
beam might be made to "punch" holes.  If the beam is condensed enough,
even a very weak laser should cut the paper, given the right "color."
But the "punchings" might have to be sucked up out of the paper with a
vacuum, if the tolerance was in the microns.

The particular chart recorder that had a similar mechanism was able to
record audio frequencies accurately and give you a hard copy on light
sensitive paper, because the degree of motion of the mirror assembly
was so very light and small (like a speaker, itself).  I don't see any
problem doing the same thing with a laser!  By the way, those chart
recorders used 11-1/4" wide paper too, if I recall, and the line, I
believe, was burned at the point of contact of the cylindrical lens
with the paper.  The laser wouldn't require that, being coherent light.

Craig Brougher